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Analysis and finite element simulations of a second‐order fluid model in a bounded domain
Author(s) -
Arada Nadir,
Correia Paulo,
Sequeira Adélia
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20236
Subject(s) - mathematics , bounded function , finite element method , domain (mathematical analysis) , inertia , mathematical analysis , reynolds number , uniqueness , viscoelasticity , compressibility , partial differential equation , mechanics , classical mechanics , physics , turbulence , thermodynamics
This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007